well maybe if there's supposed to be more theory to this then you can start by such things as the history (the robotr "arm" started in vehicle manufacturing) and work your way up to the modern systems and the controls they use. are you supposed to describe the meat and potatos of how robotic arms function or are you supposed to describe the various kinds and functions?

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"sure, you can test your combat robot on kittens... But all your going to do is make kitten juice"

I would imagine that you are supposed to talk about the forces that the lengths of the arm segments have against the joints (fulcrum force etc...). also you probably want to describe about degrees of freedom, and how different tasks would require different degrees of freedom. degrees of freedom can be described as the number of joints and also the directional capabilities of the joints.

If you want to concentrate on a particular arm, you could describe the human arm. the shoulder is a ball joint with 3 degrees of freedom (all limited to some extent). the elbow is a hinge joint with 1 degree of freedom(also limited). the forearm is capable of rotation (another degree of freedom) which runs off a different system to the elbow and the wrist. the wrist is a dual hinge joint, it moves in 2 directions and has 2 degrees of freedom. convert the joints into mechanical joints and talk about how forces affect the different parts, the limitations of the arm, the good points of it etc...

You could start on the materials that you would be using and why, calculated forces and strength of materials, what is needed, but also about the programming language. I think you would have to seek it more indepth.

Sounds to me like for the math part you will need to explain kinematics of the robot arm, both forward and inverse. I don't think you would be expected to derive the equations for inverse kinematics, but at least be expected to explain how it works.The general idea is what you can use forward to find the end position of the robot arm given you know the lengths of the joints and the angles, and inverse kinematics gives you the joint angles for a known end position.